The carrier frequency of a received signal in communications systems may vary with time. Sources of frequency variations include drifts of the frequency standards and relative motion between the transmitter and receiver. Consider, as an example, a satellite terminal mounted on a ship. As the ship rolls, pitches, yaws and heaves, the received signal frequency changes, generally in a sinusoidal fashion. The amount of frequency variation is proportional to the carrier frequency. For SHF satellite communications (7-8 GHz) in the presence of rough waters, or, high sea states, the frequency could change by hundreds of Hz in a few seconds. For example, the AS-3399/WSC antenna of the U.S. Navy's AN/WSC-6 SHF SATCOM terminal is designed for sinusoidal ship motion with an amplitude of 35.degree. and a period of 7 seconds. If the antenna is mounted at a height of 30 feet from the center of motion, the maximum Doppler at 8 GHz is about 300 Hz.
Differential phase-shift keyed (DPSK) modulation modulates or encodes a logic 0 bit as a continuation of the carrier phase representing the previous bit, and modulates a logic 1 level as a phase reversal from the carrier phase representing the previous bit. The presence of Doppler shifts introduces phase variations which tend to make DPSK demodulation or decoding more noisy. Current ship-mounted SHF satellite terminals employ a special-purpose receiver to process a beacon signal transmitted by the satellite. The received beacon signal is used to track the change in frequency attributable to the Doppler shift. The detected frequency shift is fed to the communications receiver, which compensates for the frequency change. Recently, there has been interest in low cost terminals capable of supporting communications without using a beacon receiver. Without a beacon receiver, the communications receiver must track frequency using the data signal.
Modern communications systems employ forward error-correction (FEC) coding to reduce the signal-to-noise ratio (SNR) needed to support communications. Such systems typically need a SNR per bit of only four to eight dB to achieve satisfactory performance, which is usually defined as a bit error rate (BER) of 10.sup.-5. Operation at a lower SNR, made possible by the use of coding, makes frequency tracking more difficult.
The drive for lower cost terminals has also led to smaller antennas, which transduce less signal. As a result, the data rate that can be supported is smaller. The lowest useful data rate may be, for example, 75 b/s. Low rate communications in the presence of rapidly-varying Doppler is difficult because the carrier-to-noise ratio, which is the product of the data rate and the SNR per data bit, is smaller at smaller data rates, which tends to result in larger frequency tracking errors. Furthermore, the lower data rate requires a more accurate frequency estimate since the bit duration, and therefore the integration time, is longer.